Extracting Sub-Networks from Brain Functional Network Using Graph Regularized Nonnegative Matrix Factorization

Currently,functional connectomes constructed from neuroimaging data have emerged as a powerful tool in identifying brain disorders.If one brain disease just manifests as some cognitive dysfunction,it means that the disease may affect some local connectivity in the brain functional network.That is,there are functional abnormalities in the sub-network.Therefore,it is crucial to accurately identify them in pathological diagnosis.To solve these problems,we proposed a sub-network extraction method based on graph regularization nonnegative matrix factorization(GNMF).The dynamic functional networks of normal subjects and early mild cognitive impairment(eMCI)subjects were vectorized and the functional connection vectors(FCV)were assembled to aggregation matrices.Then GNMF was applied to factorize the aggregation matrix to get the base matrix,in which the column vectors were restored to a common sub-network and a distinctive sub-network,and visualization and statistical analysis were conducted on the two sub-networks,respectively.Experimental results demonstrated that,compared with other matrix factorization methods,the proposed method can more obviously reflect the similarity between the common subnetwork of eMCI subjects and normal subjects,as well as the difference between the distinctive sub-network of eMCI subjects and normal subjects,Therefore,the high-dimensional features in brain functional networks can be best represented locally in the lowdimensional space,which provides a new idea for studying brain functional connectomes.

Data Gathering in Wireless Sensor Networks Via Regular Low Density Parity Check Matrix

A great challenge faced by wireless sensor networks(WSNs) is to reduce energy consumption of sensor nodes. Fortunately, the data gathering via random sensing can save energy of sensor nodes. Nevertheless, its randomness and density usually result in difficult implementations, high computation complexity and large storage spaces in practical settings. So the deterministic sparse sensing matrices are desired in some situations. However,it is difficult to guarantee the performance of deterministic sensing matrix by the acknowledged metrics. In this paper, we construct a class of deterministic sparse sensing matrices with statistical versions of restricted isometry property(St RIP) via regular low density parity check(RLDPC) matrices. The key idea of our construction is to achieve small mutual coherence of the matrices by confining the column weights of RLDPC matrices such that St RIP is satisfied. Besides, we prove that the constructed sensing matrices have the same scale of measurement numbers as the dense measurements. We also propose a data gathering method based on RLDPC matrix. Experimental results verify that the constructed sensing matrices have better reconstruction performance, compared to the Gaussian, Bernoulli, and CSLDPC matrices. And we also verify that the data gathering via RLDPC matrix can reduce energy consumption of WSNs.

Graph Regularized L_p Smooth Non-negative Matrix Factorization for Data Representation

This paper proposes a Graph regularized Lpsmooth non-negative matrix factorization(GSNMF) method by incorporating graph regularization and L_p smoothing constraint, which considers the intrinsic geometric information of a data set and produces smooth and stable solutions. The main contributions are as follows: first, graph regularization is added into NMF to discover the hidden semantics and simultaneously respect the intrinsic geometric structure information of a data set. Second,the Lpsmoothing constraint is incorporated into NMF to combine the merits of isotropic(L_2-norm) and anisotropic(L_1-norm)diffusion smoothing, and produces a smooth and more accurate solution to the optimization problem. Finally, the update rules and proof of convergence of GSNMF are given. Experiments on several data sets show that the proposed method outperforms related state-of-the-art methods.

THE SPECTRAL PROPERTIES OF THE ITERATION MATRIX OF REGULAR SPLITTINGS FOR AN M-MATRIX

Let A=M-N be a regular splitting of an M-matrix. We study the spectral properties of the ineration matrix M-1N. Under a mild assumption on M-1 N. some necessary and sufficent conditions such that p(M-1N)=1 are obtained and the algebraic multiplicity and the index associated with eigenvalue 1 in M-1N are considered.

Kernel matrix learning with a general regularized risk functional criterion

Kernel-based methods work by embedding the data into a feature space and then searching linear hypothesis among the embedding data points. The performance is mostly affected by which kernel is used. A promising way is to learn the kernel from the data automatically. A general regularized risk functional （RRF） criterion for kernel matrix learning is proposed. Compared with the RRF criterion, general RRF criterion takes into account the geometric distributions of the embedding data points. It is proven that the distance between different geometric distdbutions can be estimated by their centroid distance in the reproducing kernel Hilbert space. Using this criterion for kernel matrix learning leads to a convex quadratically constrained quadratic programming （QCQP） problem. For several commonly used loss functions, their mathematical formulations are given. Experiment results on a collection of benchmark data sets demonstrate the effectiveness of the proposed method.

Research of matrix converter based on asymmetric regular sampling method SPWM control strategy

Based on the topological analysis of three-phase matrix AC to AC conversion circuit, an AC to AC nine-switch matrix isequivalent to rectification part and conversion part. The Matrix converter can be viewed as AC-DC-AC converter, the asymmetricregular sampling method SPWM(Sine Pulse Width Modulation) is studied and applied in the three-phase matrix AC to AC converter,Based on Matlab/simulink the simulation of the matrix converter with such strategy is carried out. Inductive load simulation is carriedout on the matrix converter prototype. The simulation results verify the workability of the asymmetric regular sampling method SPWMstrategy for matrix converter.

修正-联合正则化的冲击载荷识别与响应重构

针对传统结构响应重构中正则化方法对冲击载荷峰值识别精度低、非加载区识别结果振荡且识别精度易受噪声干扰等问题,提出基于修正-联合正则化的冲击载荷识别与结构响应重构方法.基于状态空间模型,推导冲击载荷及结构响应的重构方程.对测量响应降噪,利用降噪后响应与识别响应的差值修正L2正则化解.联合L1正则化解的稀疏性优势,在保证冲击载荷非加载区域识别稳定的同时,获得更高精度的峰值识别结果,实现结构动态响应的重构.通过数值和实验案例验证了所提方法的有效性,对比了传递矩阵法和粒子滤波法的响应重构效果.结果表明,所提方法具有良好的抗噪性,能够较准确地识别冲击载荷,有效地重构结构动态响应.

基于两步正则化Gauss-Newton迭代算法的ECT图像重建

电容层析成像(ECT)技术求解图像重建问题属于非线性问题,并且存在严重的不适定性。为提高图像重建精度,提出了一种基于两步正则化Gauss-Newton迭代算法的ECT图像重建方法。针对标准正则化Gauss-Newton迭代算法在图像重建中存在的不收敛问题,引入了两步迭代方法;改进了正则化矩阵,提高了解估计的精确度;考虑到Gauss-Newton算法对迭代初值的依赖性,加入了同伦算法。最后,进行仿真和静态实验,并与线性反投影(LBP)算法、Landweber算法、Tikhonov正则化算法进行对比。结果表明,该方法可有效提高图像重建精度。

SIGN MATRIX, REGULAR SPLITTINGS AND MONOTONIC ENCLOSURE OF SOLUTIONS FOR NONLINEAR SYSTEM OF EQUATIONS, PARTI

In this paper we introduce the sign matrix of a nonlinear system of equations x = Gx to characterize its hybrid and asynchronous monotonicity as well as convexity. Based on the configuration of the matrix, we define a new type of regular splittings of the system with which the solvability and construction of solutions for the system are transformed to those of the couple systems of the splitting formIt is shown that this couple systems is a general model for developing monotonic enclosure methods of solutions for various types of nonlinear system of equations.

基于混合正则化方法的结构载荷识别与响应重构

针对结构载荷识别与响应重构问题中存在的不适定性,提出一种最小平方残差(least square minimal residual,LSMR)算法与Tikhonov正则化方法相结合的混合正则化方法,实现利用结构有限测点的加速度响应识别载荷并重构未知的各类型响应。首先,基于时域状态空间模型构建结构的传递矩阵,并建立载荷识别与响应重构方程;其次,采用混合正则化方法改善载荷识别问题的不适定性,得到载荷的正则化解,并结合响应重构方程的传递矩阵对结构的位移、速度和加速度响应进行重构;最后,通过简支梁数值仿真和试验分析验证所提方法的可行性。结果表明,所提方法能改善重构方程的不适定性,从而对结构未知载荷和各类型响应进行有效重构。

自适应模糊正则化椒盐噪声去除模型

为有效抑制椒盐噪声对图像信息的影响,根据椒盐噪声随机破坏图像中像素值的显著特征,本文提出一种耦合噪声检测的自适应模糊正则化噪声去除模型。一方面,基于L_(1)范数建立数据保真项,实现对图像统计分布进行有效拟合。另一方面,通过对图像中像素相似性的有效量化实现图像中噪声的检测,并将此耦合至正则项中,使得模型可依据像素点实际受噪声的污染对其施加惩罚程度,最终实现椒盐噪声的自适应模糊去除。本文采用交替方向乘子法(Alternating direction method of multipliers,ADMM)进行模型的数值结果实现,并运用峰值信噪比(Peak signal-to-noise ratio,PSNR)及结构相似性(Structural similarity,SSIM)对实验结果进行评定。实验结果表明,本文提出的模型在PSNR及SSIM方面得到显著提升,其中对于灰度图像的去噪实验PSNR最高可提高1.3dB,SSIM最高可提高0.2。

复区间矩阵的Gerschgorin圆盘定理及正则性条件

本文将矩阵特征值的Gerschgorin圆盘定理推广到复区间矩阵,给出复区间矩阵特征值的Gerschgorin圆盘区域,并证明所给复区间矩阵特征值的Gerschgorin圆盘区域包含于已有的复区间矩阵特征值的Gerschgorin方盘区域.最后,应用复区间矩阵特征值的Gerschgorin圆盘定理得到复区间矩阵正则的两个新的充分条件.

基于正则化正交非负矩阵分解的旋转目标检测方法

小样本的旋转目标检测是指在样本数少的情况下进行旋转目标检测模型的训练,深度学习在旋转目标检测领域往往需要庞大的样本数和计算算力。现有的基于机器学习的旋转目标检测方法大多有着对目标尺度和姿态敏感的缺点。因此提出一种基于正则化正交非负矩阵分解的旋转目标检测方法,来解决小样本的旋转目标检测难题。首先,针对样本不具有各种角度的图片,对样本进行旋转后进行背景填充,这样便于更好的表征学习。其次,提出一种基于正则化正交非负矩阵分解算法对旋转样本的梯度直方图特征进行表征学习。最后,为了测试算法在特征学习后的有效性,利用支持向量机对特征提取后的数据进行训练和测试。实验结果表明本文的目标检测方法在多个数据集中可以取得不错的效果。

On the Centrosymmetric and Centroskewsymmetric Solutions to a Matrix Equation over a Central Algebra

Let Ω be a finite dimensional central algebra and chart Ω≠2 .The matrix equation AXB-CXD=E over Ω is considered.Necessary and sufficient conditions for the existence of centro(skew)symmetric solutions of the matrix equation are given.As a particular case ,the matrix equation X-AXB=C over Ω is also considered.

Quantum Yang-Baxter equation and constant R-matrix over Grassmann algebra

Constant solutions to Yang-Baxter equation are investigated over Grassmann algebra for the case of 6-vertex R-matrix. The general classification of all possible solutions over Grassmann algebra and particular cases with 2,3,4 generators are studied. As distinct from the standard case, when R-matrix over number field can have a maximum 5 nonvanishing elements, we obtain over Grassmann algebra a set of new full 6-vertex solutions. The solutions leading to regular R-matrices which appear in weak Hopf algebras are considered.

A New Approximation to the Linear Matrix Equation AX = B by Modification of He’s Homotopy Perturbation Method

It is well known that the matrix equations play a significant role in engineering and applicable sciences. In this research article, a new modification of the homotopy perturbation method (HPM) will be proposed to obtain the approximated solution of the matrix equation in the form AX = B. Moreover, the conditions are deduced to check the convergence of the homotopy series. Numerical implementations are adapted to illustrate the properties of the modified method.

Rees矩阵半群的GK-维数

主要探讨Rees矩阵半群的GK-维数问题.首先刻画Rees矩阵半群的性质,含有零元的一类Rees矩阵半群S的GK-维数等于S的任意非零极大幺半群M的GK-维数.然后利用这些性质,证明一类Rees矩阵半群S有多项式增长当且仅当S的所有的子幺半群有多项式增长,推广了本原富足半群里的相关结果.

信息扩散函数在半参数地壳形变分析中的应用

提出一种利用信息扩散函数构建正则矩阵的新方法。首先,仅保留半参数模型的参数化模型部分,利用最小二乘估计获取参数模型的最小二乘残差;然后,将此残差向量作为信号,计算信号的信息扩散函数估值;最后,将信息扩散估计值作为正则矩阵的主对角元素构建正则矩阵。与时间序列法相比,新方法淡化了对信号连续性和光滑性的要求,且信息扩散函数估值本质上是残差的概率分布,相当于事先合理地确定了信号权阵,使得参数估计具有良好的稳健性。中国大陆华北块体的半参数地壳形变分析结果表明,新方法具有明显优势。

Nonnegative Matrix Factorization with Zellner Penalty

Nonnegative matrix factorization (NMF) is a relatively new unsupervised learning algorithm that decomposes a nonnegative data matrix into a parts-based, lower dimensional, linear representation of the data. NMF has applications in image processing, text mining, recommendation systems and a variety of other fields. Since its inception, the NMF algorithm has been modified and explored by numerous authors. One such modification involves the addition of auxiliary constraints to the objective function of the factorization. The purpose of these auxiliary constraints is to impose task-specific penalties or restrictions on the objective function. Though many auxiliary constraints have been studied, none have made use of data-dependent penalties. In this paper, we propose Zellner nonnegative matrix factorization (ZNMF), which uses data-dependent auxiliary constraints. We assess the facial recognition performance of the ZNMF algorithm and several other well-known constrained NMF algorithms using the Cambridge ORL database.

基于正则化理论的地应力场反演及其工程应用

为了提高地应力场反演算法对观测误差的鲁棒性,提出了基于Tikhonov正则化理论的地应力场回归系数反演算法。研究表明,随着正则化因子的增加,最小二乘法法方程系数矩阵的条件数会逐渐减小,但目标函数却在逐渐增加,拟合精度也会逐步降低。为了提高反演模型的预测精度,提出了一种构造应力随埋深线性变化的假设模型。工程实际应用结果表明,与传统的矩形构造应力模型相对比,改进反演模型预测地应力的最大误差由10.96%变为1.93%,验证了所提出改进反演模型的精确性。考虑观测噪声的影响,数值模拟结果表明,所提出的地应力回归系数反演算法具有良好的鲁棒性。